This can be done at the UniProt sparql endpoint using this query.

PREFIX up:<http://purl.uniprot.org/core/>
PREFIX rdf:<http://www.w3.org/1999/02/22-rdf-syntax-ns#>

SELECT ?protein ?sequence
WHERE {
?protein up:reviewed true .
?protein up:sequence ?sequenceConcept .
?sequenceConcept rdf:value ?sequence .
FILTER ( ! contains(?sequence, 'X')) .
FILTER ( ! contains(?sequence, 'B')) .
FILTER ( ! contains(?sequence, 'Z')) .
}

You can get a nearly FASTA file from the CSV download using this query (just strip the quotes out)

PREFIX up:<http://purl.uniprot.org/core/>
PREFIX rdf:<http://www.w3.org/1999/02/22-rdf-syntax-ns#>

SELECT ?fasta
WHERE {
?protein up:reviewed true .
?protein up:sequence ?sequenceConcept .
?sequenceConcept rdf:value ?sequence .
FILTER ( ! contains(?sequence, 'X')) .
FILTER ( ! contains(?sequence, 'B')) .
FILTER ( ! contains(?sequence, 'Z')) .
BIND(concat('>',SUBSTR(STR(?protein),33),'\n',?sequence) AS ?fasta)
}

On the UniProt website there is no way to use text search criteria to query for (or exclude) entries whose sequence contain a certain type of amino acid.

UniProtKB/Swiss-Prot release 2014_09 (due out tomorrow) will contain 2360 sequences with 'B', 'X' or 'Z'. You could either find these 2360 entries first (in a local copy of UniProtKB/Swiss-Prot) and then discard them if your website query happens to retrieve one of them, or, as you suggest, inspect the sequences of your retrieved entries and discard them if they contain the unwanted amino acids.

using my tool https://github.com/lindenb/jvarkit/wiki/UniprotFilterJS

$ cat filter.js
function accept(e)
    {
    var s = e.sequence.value.toUpperCase();
    return (s.indexOf("X")==-1 && s.indexOf("B")==-1);
    }
accept(entry);

and

curl -skL "ftp://ftp.uniprot.org/pub/databases/uniprot/current_release/knowledgebase/complete/uniprot_sprot.xml.gz" | gunzip -c |java -jar dist-1.139/uniprotfilterjs.jar  -f filter.js  > filtered.xml